1. Field of the Invention
The present invention relates generally to semiconductor devices, and more particularly, to semiconductor devices including spiral inductors and a method of making the same.
2. Description of the Related Art
In forming a semiconductor device, the use of individual devices such as transistors, resistors, inductors, etc. is indispensable. Of all these devices, inductors are typically the most difficult to make since they have the most complicated structures.
FIGS.1 to 4 are perspective views for explaining a conventional method of making inductors in a semiconductor device as disclosed in U.S. Pat. No. 3,614,554 ("Miniaturized Thin Film Inductors For Use In Integrated Circuits", application Ser. No. 770,375).
After collectors 13 of integrated circuits are formed in a semiconductor substrate 10 according to a design rule, the surface of the substrate is covered with a first insulating layer 12, and then conductive collector terminals 15 are formed which connect to the collectors 13. Then, after first through eighth lower conductive lines 14a to 14h constituting conductors are formed using metal materials (FIG. 1), an oxide film 16 is formed to cover the surface of the substrate on which the first through eighth lower conductive lines 14a to 14h are formed. Then, a bar 18 of magnetic material is formed on top of the oxide film 16 and across the first through eight lower conductive lines 14a to 14h (FIG. 2).
Thereafter, a second insulating layer 20 is formed to cover the surface of the substrate on which the bar 18 is formed. First through eighth contact holes 22a to 22h are then formed in the insulating layer 20 thereby exposing one end of each of the first through eighth lower conductive lines 14a to 14h, and ninth through fifteenth contact holes 24a to 24h are formed so as to expose the other ends of the first through eighth lower conductive lines 14a to 14h. Next, a layer of metal material is formed on the oxide film 16 to cover the contact holes. The metal layer is then patterned to form upper conductive lines 26a through 26g. A first end of each of upper conductive lines 26a-26g is connected to a first end of each of lower conductive lines 14a-14g, respectively, through contact holes 22a-22g, respectively. A second end of each of upper conductive lines 26a-26g is connected to a second end of each of lower conductive lines 14b-14h, respectively, through contact holes 24b-24h, respectively.
The first through eighth lower conductive lines 14a to 14h and the first to the seventh upper conductive lines 26a to 26g form a single inductor coil.
FIG. 5 is a sectional view of a conventional conductor taken along line a-a' of FIG. 4, wherein the same reference numerals as those used in FIGS. 1 to 4 indicate the same components.
One end of the second lower conductive line 14b is connected to the second upper conductive line 26b, and the other end thereof is connected to the first upper conductive line 26a.
There are two disadvantages to an inductor fabricated as described above.
First, when the line width of the conductive lines of the inductor coil is reduced, the self-inductance L of the inductor is reduced as explained below, even though the thicknesses of the oxide film 16 and the second insulating layer 20 remain constant.
In an inductor coil that is wound with N turns around a magnetic material having a non-magnetic permeability of .mu..sub.s and a cross-sectional area of S, current I flowing through the inductor generates a magnetic field H, and the self-inductance L is given by Equation 1. EQU L=N.mu..sub.0.mu..sub.s HS/I (Equation 1)
When two inductors are fabricated, the mutual inductance is expressed by Equation 2, wherein i is current, V is voltage, .PHI. is magnetic flux density, and n is the number of turns. EQU M.sub.21 =n.sub.2.PHI..sub.21 /i.sub.1, M.sub.21 =M.sub.12 =M, V.sub.1 /V.sub.2 =i.sub.2 /i.sub.1 (Equation 2)
From Equation 1 it is apparent that the self-inductance L is proportional to the cross-sectional area S inside the coil. Assuming that the length of the semiconductor device 10 in a direction parallel to the bar 18 is "a" and the vertical length of the contact hole is "b" (see b in FIG. 5), the cross-sectional area is S=a.times.b.
In a device fabricated as described above with reference to U.S. Pat. No. 3,614,554, the dimension "a" is related to the size of the design which the inductor occupies, and "b" is determined by the sum of the thicknesses of the oxide film 16 and the second insulating layer 20. However, even when the thicknesses of the oxide film 16 and the second insulating layer 20 are held constant, reducing the width of the upper and lower conductive lines, for example, to less than 0.5 um, can reduce the value of L because, even though "a" may depend on the area the inductor occupies, the value of"b" is constrained since it is relatively dependent upon the line width, and thus, functions as a factor in reducing the value of L.
Second, because the inductor coil disclosed in the above-referenced U.S. Pat. No. 3,614,554 does not have a circular cross section, the magnetic field changes abruptly at the sharp turns in the coil as shown at I in FIG. 5.